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Abstract

A camera module employing spherical single-element lens imaging system (SSLIS) is introduced in this study. This type of imaging system can be used in compact digital cameras or mobile phone cameras, and it provides the advantages of simple design, reduced device bulkiness, and reduced manufacturing costs. When compared with conventional camera modules, our system produces radially variant blurred images, which can be satisfactorily restored by means of a polar domain deconvolution algorithm proposed in our previous study. In this study, we demonstrate an improved version of this algorithm that enables full-field-of-view (FOV) image restoration instead of the partial FOV restoration obtained via our previous algorithm. This improvement is realized by interpolating the upper and arc-shaped boundaries of the panoramic polar image such that the ringing artifacts around the center and four boundaries of the restored Cartesian image are greatly suppressed. The effectiveness of the improved algorithm is verified by image restoration of both computer simulated images and real-world scenes captured by the spherical single lens camera module. The quality of the restored image depends on the overall sparsity of all the point spread function (PSF) block Toeplitz with circulant blocks (BTCB) matrices used to restore a radially blurred image.

PSF distribution of our SSLIS. (a) 2D view, which indicates rotational symmetry (b) 3D view of PSFs along radial direction for different semi-FOV values. (c) Spot diagrams at different semi-FOV values, the full spot size is measured and marked in each sub images, the RMS spot size are also shown.

Image captured by our spherical single-lens camera module, which includes radially variant blur. (a) Captured image in the Cartesian domain (b) Panoramic polar image stretched out from (a). The corresponding boundaries in the Cartesian and panoramic polar images have been marked as A, B, C and D. (c) Nearest neighbor interpolation for the upper and arc-shaped boundaries of the polar image.

Visual comparison between an original image and the resulting images. (a) Original image. (b) Resulting image, the polar image resolution is 321×360. (c)Resulting image, the polar image resolution is 1280×7200.

Visual comparison between restored images with and without using the ringing reduction technique.. (a) Original image captured by a DSLR. (b) A software simulated image generated by the SSLIS. (c) Restored image without using the ringing reduction technique. (d) Restored image using the ringing reduction technique.(e) Magnified image of the central region of (c). (f) Magnified image of the central region of (d). (g) Magnified image of the upper region of (c). (h) Magnified image of the upper region of (d). (i) Magnified image of the right region of (c).(j) Magnified image of the right region of (d).

The building image. Visual comparison between the restored images by different number of segmented regions. (a)Original image captured by a DSLR.. (b) A software simulated image generated by the SSLIS. (c)Restored using PSF3.(d) Restored using PSF7.(e) Restored using PSF10.(f) Restored using PSF14(g) Restored using PSF3 and PSF7. (h) Restored using PSF7 and PSF14. (i) Restored using PSF7, PSF9, PSF12 and PSF14. (j)Restored using PSF10, PSF14, PSF16 and PSF18.(k)Relationship between the overall sparsity and RMSE

The English characters image. Visual comparison between the restored images by different number of segmented regions. (a)Original computer generated image. (b) A software simulated image generated by the SSLIS. (c)Restored using PSF3.(d) Restored using PSF7.(e) Restored using PSF10.(f) Restored using PSF14(g) Restored using PSF3 and PSF7. (h) Restored using PSF7 and PSF14. (i) Restored using PSF7, PSF9, PSF12 and PSF14. (j) Restored using PSF10, PSF14, PSF16 and PSF18.(k) Relationship between the overall sparsity and RMSE